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(5x-2)(3x+5)=5x-2
We move all terms to the left:
(5x-2)(3x+5)-(5x-2)=0
We get rid of parentheses
(5x-2)(3x+5)-5x+2=0
We multiply parentheses ..
(+15x^2+25x-6x-10)-5x+2=0
We get rid of parentheses
15x^2+25x-6x-5x-10+2=0
We add all the numbers together, and all the variables
15x^2+14x-8=0
a = 15; b = 14; c = -8;
Δ = b2-4ac
Δ = 142-4·15·(-8)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{676}=26$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26}{2*15}=\frac{-40}{30} =-1+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*15}=\frac{12}{30} =2/5 $
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